Determine the period of the function: f(x)=3sin1/2x+2
The period of the parent function is 2pi. The factor of 1/2 applied to x changes the period to 2pi/(1/2) = 4pi.
The period is 2pi/b.
So when you plug it in, 2pi/1/2 would result in 2pi x 2/1. In the end it would be 4pi.
To determine the period of a function, we need to find the distance between two consecutive identical points on the graph. For a sine function of the form f(x) = A*sin(Bx + C) + D, the period is given by:
Period = 2π / |B|
In the given function f(x) = 3*sin(1/2x) + 2, we can rewrite it in the form above by factoring out 1/2 from the argument of the sine function:
f(x) = 3*sin(1/2 * x) + 2
= 3*sin(1/2x) + 2
Here, A = 3, B = 1/2, C = 0, and D = 2. Therefore, the period can be computed as:
Period = 2π / |B|
= 2π / |1/2|
= 2π * (2/1)
= 4π
Thus, the period of the function f(x) = 3sin(1/2x) + 2 is 4π.